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palais–smale sequences

Proceedings of the Edinburgh Mathematical Society (1)

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Infinitely Many Solutions for Schrödinger–Kirchhoff-Type Fourth-Order Elliptic Equations
Part of
- Elliptic equations and systems
Hongxue Song, Caisheng Chen
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 4 / November 2017

Published online by Cambridge University Press:

30 January 2017, pp. 1003-1020
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This paper deals with the class of Schrödinger–Kirchhoff-type biharmonic problems

where Δ2 denotes the biharmonic operator, and f ∈ C(ℝN × ℝ, ℝ) satisfies the Ambrosetti–Rabinowitz-type conditions. Under appropriate assumptions on V and f, the existence of infinitely many solutions is proved by using the symmetric mountain pass theorem.